Langmuir 1989,5, 273-276
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Determination of BET Surface Areas of Porous Thin Films Using Surface Acoustic Wave Devices A. J. Ricco,* G. C.Frye, and S. J . Martin Microsensor Division 11 13, Sandia National Laboratories, Albuquerque, New Mexico 87185 Received August 12, 1988. In Final Form: September 20, 1988 Surface acoustic wave (SAW) devices have been used to measure thin-fib surface area using N2adsorption isotherms for the first time. This technique is lo4 times more sensitive than conventional methods for making such measurements. The test film is deposited or formed directly on the SAW device substrate. The SAW device serves as a highly sensitive microbalance, measuring the extent of N2 adsorption as a function of N2 partial pressure; resolution is 0.35% of an N2 monolayer. The adsorption data can be used to determine surface areas by using the BET analysis or to calculate a pore size distribution for the film.
Introduction
to evaluate c = 1 + s/I and n, = l / ( s + I). The molecular
Porous thin-film materials, including polymers, ceramics, and composites, are of increasing technological and commercial importance. The full potential of such materials can be realized only if they are well characterized, and such characterization should include accurate measurement of total surface area and pore size distribution. Adsorption isotherms, in which the extent of adsorption is measured as a function of adsorbate partial pressure, are now widely used to characterize bulk porous samples.'-3 Nitrogen gas at its boiling point is the most commonly used adsorbate because it gives more consistent results than other adsorbates for a wide variety of adsorbent material^.'^^^^ Several commercial instruments are available for obtaining N2 adsorption isotherms, These instruments measure the amount of adsorbed N2 by using gravimetric, volumetric, or dynamic flow-through methods.2 To determine sample surface area, the experimental isotherm can be compared to a model, developed by Brunauer, Emmett, and Teller: which models multilayer adsorption with one binding energy between the adsorbate and the surface for the first monolayer and a second binding energy for adsorption of subsequent monolayers. The resulting isotherm can be given by4p5
A2)l and is generally independent of adsorbent properties.
in which n is the number density of adsorbed molecules, n , is the density corresponding to one monolayer on the available surfaces, p is adsorbate partial pressure, p o is adsorbate saturation pressure, and c is a constant that depends on the two binding energies. Since the amount of adsorption often depends on whether p is increasing or decreasing,' adsorption is typically monitored as p / p o increases from 0 to a value near 1 and then returns to 0. Equation 1 can be rearranged to give
When the BET model holds, a plot of p vs p / p o is a straight line whose slope (s) and intercept (I)can be used (1)Gregg, S. J.; Sing, K. S. W. Adsorption, Surface Area and Porosity; Academic: New York, 1982. (2)Lowell, S.; Shields, J. E. Powder Surface Area and Porosity; Chapman & Hall: New York, 1984. (3)Brunauer, S. Langmuir 1987,3, 3. (4)Adamson, A. W.Physical Chemistry of Surfaces, 4th ed.; Wiley: New York, 1982;Chapter XVI. (5)Brunauer, S.; Emmett, P. H.; Teller, E. J. Am. Chem. SOC.1938, 60,309.
area of an adsorbed N2 molecule is well-known (a, = 16.2 Sample surface area ( A ) is calculated by using A = n,a,. Pore size distributions can also be obtained by analyzing the isotherm to determine the volume of capillary condensation occurring as a function of p/po.'*2,6 Because current commercial technology for obtaining N2 isotherms requires a minimum sample surface area of lo4 cm2,2v4it is most readily applied to high surface area bulk samples, which often have several hundred square meters of surface area per gram. Results presented in this paper demonstrate the risk associated with drawing conclusions about thin-film surface areas on the basis of data from bulk samples, even though both samples are prepared from the same starting materials by use of a similar process. To make surface area measurements directly of thin films, where the surface area may be only 1 order of magnitude greater than the nominal film area, large areas (>lo00 cm2) of film are required. These areas can sometimes be obtained by depositing the film on a high surface area substrate. However, besides requiring additional preparation time, such samples may have surface areas which differ from that of a thin film formed on a planar substrate-the typical situation for most thin-film applications. Enhancement of the sensitivity to adsorbed N2 by several orders of magnitude would allow full characterization of the surface area and pore size distribution of as-deposited thin films. Recently, the extreme sensitivity of surface acoustic wave (SAW) devices to small changes in adsorbed mass has been utilized to construct a variety of chemical sensor~.'-'~ Measurement of as little as 100 pg/cm2, corresponding to 0.35% of a monolayer of N2 on the flat SAW device substrate, has been demonstrated in this laboratory.13J4 A related device, the quartz crystal microbalance (QCM), has been used to monitor adsorption of various (6) Glaves, C. L.; Frye, G. C.; Smith, D. M.; Brinker, C. J.; Datye, A.; Ricco, A. J.; Martin, S. J., submitted to Langmuir. (7) Martin,S. J.; Schweizer, K. S.; Schwartz, S. S.; Gunshor, R. L. Proc. 1984 IEEE Ultrasonics Symp.; I E E E New York, 1984;pp 207-212. (8)Chuang, C. T.; White, R. M. Proc. 1982 IEEE Ultrasonics Symp.; I E E E New York, 1982; pp 295-298. (9)Snow, A.; Wohltjen, H. Anal. Chem. 1984,56, 1411. (10)D'Amico, A.; Palma, A.; Verona, E. Sensors and Actuators 1982, 3, 31. (11)Venema, A. et al. IEEE Trans.Ultrasonics, Ferroelectrics, and Freq. Contr. 1987,UFFC-34, 149. (12)Bryant, A.;Lee, D. L.; Vetelino, J. F. Proc. 1981IEEE Ultrasonics Symp.; IEEE: New York, 1981;pp 171-174. (13)Frye, G.C.; Ricco, A. J.; Martin, S. J.; Brinker, C. J. Mat. Res. Soc. Symp. Proc.; Materials Research SOC.: Pittsburgh, 1988;Vol. 121, p p 349-354. (14)Martin, S.J.; Ricco, A. J.; Ginley, D. S.; Zipperian, T. E. IEEE Trans. Ultrasonics, Ferroelectrics and Freq. Contr. 1987,UFFC-34, 142.
0743-7463/89/2405-0273$01.50/0 0 1989 American Chemical Society
274 Langmuir, Vol. 5, No. I , 1989
Letters stability over short time intervals (1min) is on the order of 1 Hz or less, allowing detection of 10 ppb changes in wave velocity (or 77 pg/cm2). In this letter, we describe the use of SAW devices to measure the mass changes accompanying the adsorption of Nz a t 77 K by thin films as a function of Nz partial pressure. Subsequent BET analysis of adsorption data obtained with this technique yields film surface area values, in cm2/cm2of nominal film area, from near unity to almost 50.
DEWAR WITH LIQUID NITROGEN
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Figure 1. Schematic of a surface acoustic wave device in the experimental setup for obtaining 77 K N2 adsorption isotherms. The N2 fractional saturation pressure is varied under computer control by dilution with He over the range 0-0.95.
species onto metal substrates.'"" In comparison to the QCM,SAW devices provide enhanced sensitivity as a result of higher operating frequencies and confinement of the wave energy to within one wavelength of the surface.18J9 An additional advantage for the study of some thin-film materials is the fact that films are deposited on the oxide surface (e.g., S O 2 ,LiNb03, or ZnO) of the SAW substrate rather than on the metal electrode of the QCM. The typical configuration of a SAW device is shown in Figure 1. Two interdigital transducers at opposite ends of a piezoelectric substrate excite and detect a SAW, also known as a Rayleigh wave. An oscillating electrical potential applied to the input transducer creates a n oscillating strain field in the piezoelectric substrate, launching the acoustic wave. After traversing the length of the crystal, the mechanical oscillations are converted back into an electrical signal by the output transducer. Because nearly all the SAW energy is carried within one wavelength of the surface, the SAW velocity is sensitive to extremely small changes in surface parameters.l9 A simple and highly accurate way to monitor acoustic wave velocity is to incorporate the SAW device as the feedback element of an oscillator loop, as shown in Figure 1. When the net gain of the loop equals unity, the loop will spontaneously oscillate at a frequency for which the round-trip phase shift is a multiple of 2n. Since separation between input and output transducers is many wavelengths, the majority of the loop phase shift occurs in the SAW device. Consequently, SAW propagation velocity controls the oscillation frequency. When perturbation of the SAW velocity is due only to mass loading variation, frequency changes are related to the amount of adsorbed nitrogen by
(3) in which K is the fraction of the SAW path length between transducers covered by the film ( K = 1in the present case), c, is the mass sensitivity of the device (1.3 X lo* cm2.s/g for ST-quartz),19uo and f o are the unperturbed wave velocity and oscillator frequency, respectively, and m is the mass of adsorbed Nz molecules/sensor area. Frequency (15) Lee, W.Y.; Slutsky, L.J. J . Phys. Chem. 1982, 86, 842. (16) Krim. J. Thin Solid Films 1986. 137. 297. (17) Migone, A. D.;Dash, J. G.; Schidk, M'.;Vilches, 0. E. Phys. Reu. B: Condens. Matter 1986, 34, 6322. (18) Ricco, A. J.; Martin, S.J. Proc. Symp. on Electroless Dep. of Metah and Alloys; Electrochem. SOC.:Pennington, NJ, 1988, Vol. 88-12; pp 142-153. (19) Auld, B. A. Acoustic Waues and Fields in Solids; Wiley: New York, 1973; Vol. 2.
SAW devices were designed at Sandia Labs and fabricated on ST-cut quartz substrates by Crystal Technologies, Inc. (Palo Alto, CA). Devices have two interdigital transducers, each composed of 50 finger-pairs with 32-pm periodicity; uo is 3100 m/s, yielding a center frequency of 97 MHz. Transducers are defined photolithographically from 200-nm-thickAu on Cr metallization; the finger length is 1.7 mm. Center-to-center separation between transducers is 7.36 mm. The SAW device is mounted in a 25 X 13mm flatpack installed in a brass test case covered by a stainless steel lid containing a gas inlet and outlet. A Teflon gasket provides a gas-tight seal between the edge of the flatpack and the lid. An oscillator loop is formed by connecting the input and output transducers of the SAW device via a wide-band amplifier;a fraction of the oscillator signal is fed to a frequency counter interfaced with a computer for data acquisition. A more detailed description of the electronic system is given elsewhere?O To maintain the device at 77 K, the test case and a stainless steel or copper coil connected to the gas inlet are immersed in liquid nitrogen contained in a Dewar flask (Figure 1). By use of mass flow controllers to set flow rates, the partial pressure of N2 in a nonadsorbing2He carrier stream is varied under computer control (flow rates are adjusted every 3 s). The oscillation frequency is monitored as p / p o increases from 0 (pure He) to 0.95 and then returns to 0. Isotherms are obtained over the course of 2 h; measurements made on shorter and longer time scales have shown this rate of change to be sufficiently slow for equilibrium to be maintained throughout the isotherm. The relatively short equilibration time is consistent with the shorter thermal diffusion time pertinent to a continuous thin film in intimate contact with a comparatively massive thermal reservoir (the substrate). Thus, the latent heat of adsorption is more quickly dissipated than for bulk samples, allowing more rapid measurements. Two silicate-based sol-gel systems, one yielding fairly high surface areas and the other giving minimal porosities, were used to synthesizethin films for isothermal measurements. Films were formed by dip coating a SAW device, followed by a 5-min anneal at 400 "C. The high-porosity sample, a 1650-A-thickfilm with a refractive index of 1.21, is denoted four-component because it consists of SiOz,B203,A1203, and BaO in a ratio (by weight) of 71:18:7:4. The solution was prepared by using the alkoxides of Si, Al, and B and the acetate of Ba. The reaction conditions were identical with those described in detail e1sewhere:l except that the solution used here was Na+-free. The solution was aged 2 weeks at pH 3 and 50 "C before dip coating at 20 cm/min. For the low-porosity sample, denoted A2, an acid-catalyzedhydrolysis of tetraethoxysilane in ethanol was used.22 The solution was diluted 1:2 (A2:ethanol by volume) and dip coated at 5 cm/min to yield a 600-8, film with a refractive index of 1.39. For purposes of comparison, a bulk sample was obtained by allowing the A2 solution to gel at room temperature (3 days), followed by drying at 50 "C. For the A2 bulk sample, N2adsorption isotherms were obtained by using a Micromeritics Digisorb 2600. The Digisorb software (utilizing the BET equation) was used to calculate surface areas based on the isotherm from p / p o = 0.05-0.21, and the amount of nitrogen adsorbed for p / p o > 0.995 was used to evaluate po(20) Ricco, A.J.; Martin, S.J.; Zipperian, T. E. Sensors and Actuators 1985, 8,319. (21) Brinker, C. J.; Mukherjee, S. P. J. Mater. Sci. 1981, 16,1980. (22) Brinker, C. J.; Keefer, K. D.; Schaefer, D. W.; Ashley, C. S. J . Non-Cryst. Solids 1982, 48, 47.
Letters
Langmuir, Vol. 5, No. 1, 1989 275 5000
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